Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 30
sizeStates = 7
sizeConstants = 22
from math import *
from numpy import *
def createLegends():
legend_states = [""] * sizeStates
legend_rates = [""] * sizeStates
legend_algebraic = [""] * sizeAlgebraic
legend_voi = ""
legend_constants = [""] * sizeConstants
legend_voi = "t in component environment (second)"
legend_constants[0] = "C_m in component environment (fF)"
legend_states[0] = "q_K_o in component environment (fmol)"
legend_states[1] = "q_K_i in component environment (fmol)"
legend_states[2] = "q_Sa in component environment (fmol)"
legend_states[3] = "q_Sb in component environment (fmol)"
legend_states[4] = "q_Sc in component environment (fmol)"
legend_states[5] = "q_Sd in component environment (fmol)"
legend_states[6] = "q_mem in component environment (fC)"
legend_constants[1] = "R in component environment (J_per_K_per_mol)"
legend_constants[2] = "T in component environment (kelvin)"
legend_constants[3] = "F in component environment (C_per_mol)"
legend_algebraic[21] = "v_Kr in component Kr (fmol_per_sec)"
legend_algebraic[27] = "I_mem_Kr in component Kr (fA)"
legend_algebraic[1] = "I_stim in component environment (fA)"
legend_constants[4] = "stimPeriod in component environment (second)"
legend_constants[5] = "stimDuration in component environment (second)"
legend_algebraic[0] = "tPeriod in component environment (second)"
legend_constants[6] = "kappa_Kr in component Kr_parameters (fmol_per_sec)"
legend_constants[7] = "kappa_xr10 in component Kr_parameters (fmol_per_sec)"
legend_constants[8] = "kappa_xr11 in component Kr_parameters (fmol_per_sec)"
legend_constants[9] = "kappa_xr20 in component Kr_parameters (fmol_per_sec)"
legend_constants[10] = "kappa_xr21 in component Kr_parameters (fmol_per_sec)"
legend_constants[11] = "K_K_i in component Kr_parameters (per_fmol)"
legend_constants[12] = "K_K_o in component Kr_parameters (per_fmol)"
legend_constants[13] = "K_Sa_Kr in component Kr_parameters (per_fmol)"
legend_constants[14] = "K_Sb_Kr in component Kr_parameters (per_fmol)"
legend_constants[15] = "K_Sc_Kr in component Kr_parameters (per_fmol)"
legend_constants[16] = "K_Sd_Kr in component Kr_parameters (per_fmol)"
legend_constants[17] = "zK in component Kr_parameters (dimensionless)"
legend_constants[18] = "z_xr1_f in component Kr_parameters (dimensionless)"
legend_constants[19] = "z_xr1_r in component Kr_parameters (dimensionless)"
legend_constants[20] = "z_xr2_f in component Kr_parameters (dimensionless)"
legend_constants[21] = "z_xr2_r in component Kr_parameters (dimensionless)"
legend_algebraic[2] = "u_K_i in component Kr (J_per_mol)"
legend_algebraic[3] = "u_K_o in component Kr (J_per_mol)"
legend_algebraic[4] = "V_mem in component Kr (J_per_C)"
legend_algebraic[5] = "Am_Kr in component Kr (J_per_mol)"
legend_algebraic[19] = "Af_Kr in component Kr (J_per_mol)"
legend_algebraic[20] = "Ar_Kr in component Kr (J_per_mol)"
legend_algebraic[17] = "v_Sa in component Kr (fmol_per_sec)"
legend_algebraic[28] = "v_Sb in component Kr (fmol_per_sec)"
legend_algebraic[26] = "v_Sc in component Kr (fmol_per_sec)"
legend_algebraic[29] = "v_Sd in component Kr (fmol_per_sec)"
legend_algebraic[12] = "v_x10 in component Kr (fmol_per_sec)"
legend_algebraic[24] = "v_x11 in component Kr (fmol_per_sec)"
legend_algebraic[16] = "v_x20 in component Kr (fmol_per_sec)"
legend_algebraic[25] = "v_x21 in component Kr (fmol_per_sec)"
legend_algebraic[6] = "mu_Sa in component Kr (J_per_mol)"
legend_algebraic[9] = "mu_Sb in component Kr (J_per_mol)"
legend_algebraic[13] = "mu_Sc in component Kr (J_per_mol)"
legend_algebraic[18] = "mu_Sd in component Kr (J_per_mol)"
legend_algebraic[7] = "Af_x10 in component Kr (J_per_mol)"
legend_algebraic[10] = "Ar_x10 in component Kr (J_per_mol)"
legend_algebraic[14] = "Af_x11 in component Kr (J_per_mol)"
legend_algebraic[22] = "Ar_x11 in component Kr (J_per_mol)"
legend_algebraic[8] = "Af_x20 in component Kr (J_per_mol)"
legend_algebraic[15] = "Ar_x20 in component Kr (J_per_mol)"
legend_algebraic[11] = "Af_x21 in component Kr (J_per_mol)"
legend_algebraic[23] = "Ar_x21 in component Kr (J_per_mol)"
legend_rates[1] = "d/dt q_K_i in component environment (fmol)"
legend_rates[0] = "d/dt q_K_o in component environment (fmol)"
legend_rates[6] = "d/dt q_mem in component environment (fC)"
legend_rates[2] = "d/dt q_Sa in component environment (fmol)"
legend_rates[3] = "d/dt q_Sb in component environment (fmol)"
legend_rates[4] = "d/dt q_Sc in component environment (fmol)"
legend_rates[5] = "d/dt q_Sd in component environment (fmol)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
constants[0] = 60000
states[0] = 20.0448
states[1] = 388.832
states[2] = 1.598306E-07
states[3] = 1.598306E-07
states[4] = 1.598306E-07
states[5] = 1.598306E-07
states[6] = -13039
constants[1] = 8.31
constants[2] = 310
constants[3] = 96500
constants[4] = 1
constants[5] = 0.0001
constants[6] = 175.029
constants[7] = 0.0794844
constants[8] = 0.00212813
constants[9] = 0.267259
constants[10] = 2.18134
constants[11] = 12.9706
constants[12] = 95.1175
constants[13] = 0.0465841
constants[14] = 0.00570751
constants[15] = 1.73989
constants[16] = 0.213172
constants[17] = 1
constants[18] = 1.6149028778859738
constants[19] = -1.3218634652232777
constants[20] = -1.0273976425216251
constants[21] = -0.18153135376657775
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[4] = states[6]/constants[0]
algebraic[6] = constants[1]*constants[2]*log(constants[13]*states[2])
algebraic[7] = algebraic[6]+constants[18]*constants[3]*algebraic[4]
algebraic[9] = constants[1]*constants[2]*log(constants[14]*states[3])
algebraic[10] = algebraic[9]+constants[19]*constants[3]*algebraic[4]
algebraic[12] = constants[7]*(exp(algebraic[7]/(constants[1]*constants[2]))-exp(algebraic[10]/(constants[1]*constants[2])))
algebraic[8] = algebraic[6]+constants[20]*constants[3]*algebraic[4]
algebraic[13] = constants[1]*constants[2]*log(constants[15]*states[4])
algebraic[15] = algebraic[13]+constants[21]*constants[3]*algebraic[4]
algebraic[16] = constants[9]*(exp(algebraic[8]/(constants[1]*constants[2]))-exp(algebraic[15]/(constants[1]*constants[2])))
algebraic[17] = -algebraic[12]-algebraic[16]
rates[2] = algebraic[17]
algebraic[5] = constants[17]*constants[3]*algebraic[4]
algebraic[2] = constants[1]*constants[2]*log(constants[11]*states[1])
algebraic[18] = constants[1]*constants[2]*log(constants[16]*states[5])
algebraic[19] = algebraic[18]+algebraic[2]+algebraic[5]
algebraic[3] = constants[1]*constants[2]*log(constants[12]*states[0])
algebraic[20] = algebraic[18]+algebraic[3]
algebraic[21] = custom_piecewise([equal(algebraic[5] , 0.00000), 1.00000*constants[6]*(exp(algebraic[19]/(constants[1]*constants[2]))-exp(algebraic[20]/(constants[1]*constants[2]))) , True, (((1.00000*constants[6]*algebraic[5])/(constants[1]*constants[2]))/(exp(algebraic[5]/(constants[1]*constants[2]))-1.00000))*(exp(algebraic[19]/(constants[1]*constants[2]))-exp(algebraic[20]/(constants[1]*constants[2])))])
rates[1] = -algebraic[21]
rates[0] = algebraic[21]
algebraic[14] = algebraic[13]+constants[18]*constants[3]*algebraic[4]
algebraic[22] = algebraic[18]+constants[19]*constants[3]*algebraic[4]
algebraic[24] = constants[8]*(exp(algebraic[14]/(constants[1]*constants[2]))-exp(algebraic[22]/(constants[1]*constants[2])))
algebraic[26] = algebraic[16]-algebraic[24]
rates[4] = algebraic[26]
algebraic[11] = algebraic[9]+constants[20]*constants[3]*algebraic[4]
algebraic[23] = algebraic[18]+constants[21]*constants[3]*algebraic[4]
algebraic[25] = constants[10]*(exp(algebraic[11]/(constants[1]*constants[2]))-exp(algebraic[23]/(constants[1]*constants[2])))
algebraic[27] = constants[3]*(-constants[17]*algebraic[21]+algebraic[12]*(constants[19]-constants[18])+algebraic[24]*(constants[19]-constants[19])+algebraic[16]*(constants[21]-constants[20])+algebraic[25]*(constants[21]-constants[20]))
algebraic[0] = voi-floor(voi/constants[4])*constants[4]
algebraic[1] = custom_piecewise([greater_equal(algebraic[0] , 0.300000) & less_equal(algebraic[0] , 0.300000+constants[5]), (0.0750000*constants[0])/constants[5] , True, 0.00000])
rates[6] = algebraic[27]+algebraic[1]
algebraic[28] = algebraic[12]-algebraic[25]
rates[3] = algebraic[28]
algebraic[29] = algebraic[24]+algebraic[25]
rates[5] = algebraic[29]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[4] = states[6]/constants[0]
algebraic[6] = constants[1]*constants[2]*log(constants[13]*states[2])
algebraic[7] = algebraic[6]+constants[18]*constants[3]*algebraic[4]
algebraic[9] = constants[1]*constants[2]*log(constants[14]*states[3])
algebraic[10] = algebraic[9]+constants[19]*constants[3]*algebraic[4]
algebraic[12] = constants[7]*(exp(algebraic[7]/(constants[1]*constants[2]))-exp(algebraic[10]/(constants[1]*constants[2])))
algebraic[8] = algebraic[6]+constants[20]*constants[3]*algebraic[4]
algebraic[13] = constants[1]*constants[2]*log(constants[15]*states[4])
algebraic[15] = algebraic[13]+constants[21]*constants[3]*algebraic[4]
algebraic[16] = constants[9]*(exp(algebraic[8]/(constants[1]*constants[2]))-exp(algebraic[15]/(constants[1]*constants[2])))
algebraic[17] = -algebraic[12]-algebraic[16]
algebraic[5] = constants[17]*constants[3]*algebraic[4]
algebraic[2] = constants[1]*constants[2]*log(constants[11]*states[1])
algebraic[18] = constants[1]*constants[2]*log(constants[16]*states[5])
algebraic[19] = algebraic[18]+algebraic[2]+algebraic[5]
algebraic[3] = constants[1]*constants[2]*log(constants[12]*states[0])
algebraic[20] = algebraic[18]+algebraic[3]
algebraic[21] = custom_piecewise([equal(algebraic[5] , 0.00000), 1.00000*constants[6]*(exp(algebraic[19]/(constants[1]*constants[2]))-exp(algebraic[20]/(constants[1]*constants[2]))) , True, (((1.00000*constants[6]*algebraic[5])/(constants[1]*constants[2]))/(exp(algebraic[5]/(constants[1]*constants[2]))-1.00000))*(exp(algebraic[19]/(constants[1]*constants[2]))-exp(algebraic[20]/(constants[1]*constants[2])))])
algebraic[14] = algebraic[13]+constants[18]*constants[3]*algebraic[4]
algebraic[22] = algebraic[18]+constants[19]*constants[3]*algebraic[4]
algebraic[24] = constants[8]*(exp(algebraic[14]/(constants[1]*constants[2]))-exp(algebraic[22]/(constants[1]*constants[2])))
algebraic[26] = algebraic[16]-algebraic[24]
algebraic[11] = algebraic[9]+constants[20]*constants[3]*algebraic[4]
algebraic[23] = algebraic[18]+constants[21]*constants[3]*algebraic[4]
algebraic[25] = constants[10]*(exp(algebraic[11]/(constants[1]*constants[2]))-exp(algebraic[23]/(constants[1]*constants[2])))
algebraic[27] = constants[3]*(-constants[17]*algebraic[21]+algebraic[12]*(constants[19]-constants[18])+algebraic[24]*(constants[19]-constants[19])+algebraic[16]*(constants[21]-constants[20])+algebraic[25]*(constants[21]-constants[20]))
algebraic[0] = voi-floor(voi/constants[4])*constants[4]
algebraic[1] = custom_piecewise([greater_equal(algebraic[0] , 0.300000) & less_equal(algebraic[0] , 0.300000+constants[5]), (0.0750000*constants[0])/constants[5] , True, 0.00000])
algebraic[28] = algebraic[12]-algebraic[25]
algebraic[29] = algebraic[24]+algebraic[25]
return algebraic
def custom_piecewise(cases):
"""Compute result of a piecewise function"""
return select(cases[0::2],cases[1::2])
def solve_model():
"""Solve model with ODE solver"""
from scipy.integrate import ode
# Initialise constants and state variables
(init_states, constants) = initConsts()
# Set timespan to solve over
voi = linspace(0, 10, 500)
# Construct ODE object to solve
r = ode(computeRates)
r.set_integrator('vode', method='bdf', atol=1e-06, rtol=1e-06, max_step=1)
r.set_initial_value(init_states, voi[0])
r.set_f_params(constants)
# Solve model
states = array([[0.0] * len(voi)] * sizeStates)
states[:,0] = init_states
for (i,t) in enumerate(voi[1:]):
if r.successful():
r.integrate(t)
states[:,i+1] = r.y
else:
break
# Compute algebraic variables
algebraic = computeAlgebraic(constants, states, voi)
return (voi, states, algebraic)
def plot_model(voi, states, algebraic):
"""Plot variables against variable of integration"""
import pylab
(legend_states, legend_algebraic, legend_voi, legend_constants) = createLegends()
pylab.figure(1)
pylab.plot(voi,vstack((states,algebraic)).T)
pylab.xlabel(legend_voi)
pylab.legend(legend_states + legend_algebraic, loc='best')
pylab.show()
if __name__ == "__main__":
(voi, states, algebraic) = solve_model()
plot_model(voi, states, algebraic)